Matstat seminarium tisdagen 29 maj 2001 kl. 13.15

Charles-Antoine Guerin, p.t. Chalmers

 Electromagnetic scattering  on fractional Brownian surfaces
 and estimation of the Hurst exponent.

Abstract:

Fractional Brownian motion is known to be a realistic model for many
natural rough surfaces. It is defined by means of a single parameter, the
Hurst exponent, which determines the fractal characteristics of the
surface. We propose a method to estimate the Hurst exponent of a
fractional Brownian profile from the electromagnetic scattering data. The
method is developed in the framework of three usual approximations, with
different domains of validity: the Kirchhoff Approximation, the Small
Slope Approximation of Voronovitch and the Small Perturbation Method. A
universal power-law dependence upon the incident wavenumber is shown to
hold for the scattered far-field intensity, irrespectively of the
considered approximation and the polarization, with a common scaling
exponent trivially related to the Hurst exponent.
This leads naturally to an estimator of the latter based on a log-log
regression of the far-field intensity at fixed scattering angle. We
discuss the performances of this estimator and propose an improved version
by allowing the scattering angle to vary. The theoretical performances of
these estimators are then checked by numerical simulations. Finally, we
present a rigorous numerical computation of the scattered intensity in the
resonance domain, where none of the aforementioned approximations applies.
The numerical results show the persistence of a power-law behavior, but
with a different and still non-trivial exponent.